Welcome to the forum.
The definition of persistent infection, whether HPV or anything else, is pretty straightforward. It means the infectious agent remains in the body. For HPV, however, it's a bit complicated. Some HPV infections persist in the forum of viral DNA, which can't be transmitted and never cause disease. Whether you call this "persistence" or not is a matter of semantics, not biology. If it never causes a problem and is kept in check by the immune system, who cares?
Whether or not you have persistent HPV, and whether it is causing recurrent warts, is not something I can answer based on the information provided. That the recurrent lesions are similar in appearance to the original one is not, it itself, very reliable. To your specific questions:
1) The HPV types that cause warts rarely cause cancer; and the cancer-causing ones rarely cause warts. I can't say whether your lesions mark you as being at greater risk of genital cancer; this is a question for a dermatologist after personal evaluation. not online investigation. However, I would reassure you that HPV related genital skin cancers are rarely dangerous; as long as you are on the alert for new lesions so that they can be excised (or otherwise treated), the chance of a serious outome is very , very low. This is something to pay attention to, but not to be a cause of serious alarm.
2) I don't understand what you're asking. If you have an active HPV infection, you can transmit it to partners by the activities mentioned. But the risk to you for new HPV infections, or of cancer, is no higher than if you had no HPV at all. Even though some oral cancers due to HPV-16 are rising in frequency, these remain rare cancers. See the thread linked below:
http://www.medhelp.org/posts/STDs/HPV-and-oral-sex/show/1515473
3) As noted above, different HPV types cause warts and cancer. This remains a question for a dermatologist, not an STD expert.
4) I don't know the answer to this. Again, a dermatologic question, not one an STD expert is likely to know. (When we see unusual or recurrent penile lesions that may be recurrent warts or cancer in an STD clinic, we refer them to dermatologists.)
5) Once again, a dermatology question. This doesn't sound at all alarming, however, and I doubt it has anything to do with HPV.
I hope this has helped. Best wishes-- HHH, MD